00868nas a2200109   4500008004300000245007300043210006900116520049600185100002400681700001700705856003600722       2006                        en_Ud  00aForced vibrations of wave equations with non-monotone nonlinearities0 aForced vibrations of wave equations with nonmonotone nonlinearit3 aWe prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz.1 aBerti, Massimiliano1 aBiasco, Luca  uhttp://hdl.handle.net/1963/2160